Each of the “golden arches” at a McDonald’s restaurant is in the shape of a
parabola. Each arch is
modeled by the equation h (t )=−t2
feet and t
is the
distance, in feet, from one side of the arch.
a) What is the axis of symmetry for this parabola?
b) What is the vertex of this parabola?
c) What is the maximum height of one of the golden arches.
d) How wide is one of the arches at its base?
+6 t , where h(t ) is the height of the arch in

A) t = 3 feet

B) The vertex = (3 , 9)

C) maximum height = 9 feet

D) Base Width = 6 feet

Step-by-step explanation: Given that each arch is modeled by the equation h (t ) = −t^2 + 6t

A) the axis of symmetry for this parabola can be calculated by using the formula

t = -b/2a

Where a = -1 , b = 6

t = -6/2(-1) = 3 feet

B)  If the quadratic is written in the form y = a(x – h)^2 + k, then the vertex is the point (h, k). From equation h (t ) = −t^2 + 6t

Let h(t) = 0

−t^2 + 6t = 0

Using completing the square method

t^2 - 6t = 0

t^2 -6t + 3^2 = 3^2

(t - 3)^2 = 9

(t - 3)^2 - 9 = 0

But 0 = h(t) therefore

h(t) = (t - 3)^2 - 9

h(t) = -(t - 3)^2 + 9

Where h = 3, k = 9

The vertex = (3 , 9)

C) the maximum height of one of the golden arches will be equal to K or substitute t = 3 in the equation below

h (t ) = −t^2 + 6t

h (t ) = −3^2 + 6(3)

h(t) = -9 + 18

h(t) = 9 feet.

D) How wide is one of the arches at its base depends on the t. Assuming it is a perfect parabola, then

Width = 2h = 2×3 = 6 feet

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answer: group b.

step-by-step explanation: